9. LOGICAL VENN DIAGRAMS
This section deals with questions which aim at analysing a candidate's ability
to relate a certain given group of items and illustrate it diagrammatically.
Here are a few different types of Venn diagrams with their implications made clear.
Suppose you are given a group of three items. Then,
1. if the items evidently belong to three different groups,
the Venn diagram representing it would be as shown
alongside.
Ex. Doctors, Engineers, L a w y e r s
These three items bear no relationship to each other.
So, they are represented by 3 disjoint figures as shown
in Fig. 1.
2. if one item belongs to the class of the second and
the second belongs to the class of third, then the
representation is in the form of three concentric circles,
as shown in Fig. 2.
Ex. Seconds, Minutes, Hours
Clearly, seconds are a part of minutes and minutes
are a part of hours. So, the Venn diagram would be
as shown in the adjoining figure with circle A representing Seconds, circle B representing Minutes
and circle C representing Hours.
3. if two separate items belong to the class of the third,
they are represented by two disjoint circles inside a
bigger circle as shown in Fig. 3.
Ex. Table, Chair, Furniture
Clearly, table and chair are separate items but both
are items of furniture. So, they would be represented
as in the adjoining figure with circle A representing
Table, circle B representing Chair and circle C representing
Furniture.
4. if two items belong to the class of the third such that
. some items of each of these two groups are common
in relationship, then they are represented by two
intersecting circles enclosed within a bigger circle.
Ex. Males, Fathers, Brothers
Clearly, some fathers may be brothers. So, fathers and
brothers would be represented by two intersecting
circles. Also both fathers and brothers are males.
So, the diagrammatic representation would be as shown
in Fig. 4, with circle A representing Fathers, circle
B representing Brothers and circle C representing
Males.
2
Fig. 3
Fig. 4
5. if two items are partly related to the third, and are
themselves independent of each other they are represented by three intersecting circles in a line.
Ex. Dogs, Pet*, Cats
Clearly, some dogs and some cats are pets. But, all
the pets are not dogs or cats. Also, dogs and cats
are not related to each other. So, the given items
would be represented as shown in Fig. 5 with circle
A representing Dogs, circle B representing Pets and
circle C representing Cats.
Fig. 5
6. if (he three items are partly related to each other, they
are represented as shown in the adjoining figure.
Ex. Clerks, Government Employees, Educated
Persons
Clearly, some clerks may be government employees
and some may be educated. Similarly, some government employees may be clerks and some may be
educated. Also, some educated persons may be clerks
and some may be government employees. So, the
given items may be represented as shown in Fig. 6
with three different circles denoting the three classes.
Fig. 6
7. if one item belongs to the class of second while third
item is entirely different from the two, then they
may be represented by the adjoining diagram.
Ex. Engineers, Human Beings, Rats
Clearly, all engineers are human beings. This would
be represented by two concentric circles. But the
class of rats is entirely different from these two.
Thus, these items would be represented as shown in
Fig. 7 with circle A representing Engineers, circle B representing Human Beings and circle C representing
Fig. 7
Rats.
8. if one item belongs to the class of second and the
third item is partly related to these two, they are
represented as shown alongside.
Ex. Females, Mothers, Doctors
Clearly, all mothers are females. This would be
represented by two concentric circles. But, some
females and some mothers can be doctors. So, the
circle representing doctors would intersect the two
concentric circles. Thus, the diagram becomes as
shown in Fig. 8 with circle A representing Mothers,
circle B representing Females and circle C representing
Doctors.
Fig. 8
9. if one item belongs to the class of second and the third item is partly related
to the second, they are represented as shown alongside.
Ex. Grass-eating Animals, Cows, Flesh-eating Animals
Clearly, cows are grass-eating animals. So, they would
be'represented by two concentric circles. But some
grass-eating animals are flesh-eating also. Thus, the
Venn diagram is as shown in Fig. 9 with circle A
representing Cows, circle B representing Grass<ating
Animals and circle C representing Flesh-eating
Animals.
EXERCISE 9A
1. Which of the following diagrams correctly represents Elephants. Wolves, Animals ?
(I.A.S. 1992)
©
ODO
CM)
(a)
l b)
(c)
(d)
2. Which one of the following Venn diagrams correctly illustrates the relationship
among the classes : Carrot; Food, Vegetable ?
(I.A.S. 1996)
©
(b)
ODO
(c)
(d)
Directions (Questions 3 to 7) i In the following questions, three classes
are given. Out of the four figures that follow, you are to indicate which figure
will best represent the relationship amongst the three classes.
(a)
(b)
3. Women, Mothers, Widows
4. Authors, Teachers, Men
5. Sparrows, Birds, Mice
6. Tea, Coffee, Beverages
7. Boys, Students, Athletes
(c)
8. Select from the given diagrams, the one that illustrates the relationship among
(8.CJLA. 1994)
the given three classes : Judge; Thief, Criminal.
(a)
^
(b)
(c)
(id)
9. Choose from the four diagrams given below, the one that illustrates the relationship among Languages, French, German.
© o ODO
(a)
©
(6)
®
(c)
(rf)
10. Which one of the following diagrams correctly represents the relationship among
the classes : Tennis fans, Cricket players, Students ?
^
©
(a)
a ®
(c)
(b)
(LAJB. 1990)
(d)
I I . Which one of the following Venn diagrams best illustrates the three classes
Rhombus,
(a)
Quadrilaterals,
-
Polygons
(6)
?
(c)
99
(d)
Directions (Questions 12 to 15) : Each of these questions below contains
three groups of things. You are to choose from the following five numbered
diagrams, the diagram that depicts the correct relationship among the three
groups of things in each question.
(S.B.I.P.O. 1995)
12.
13.
14.
15.
(a)
(6)
Tables, Chairs, Furniture
Tie. Shirt, Pantaloon
Dogs, Pets. Cats
Brinjal, Meat, Vegetables
(c)
(rf)
(e)
Directions (Questions 16 to 28) : Each one of the following questions con*
tains three items. Using the relationship between these items, match each
question with the most suitable diagram. Your answer is the letter denoting
that diagram.
OBO
(a)
16.
17.
18.
19.
20.
21.
$2.
23.
24.
25.
26.
27.
28.
29.
(6)
(d)
© o
(e)
Deer, Rabbit, Mammal
Human beings, Teachers, Graduates
(Central Excise, 1995)
Whales, Fishes, Crocodiles
Plums, Tomatoes, Fruits
Mountains, Forests, Earth
Tiger, Fox, Carnivores
Grams, Beans, Legumes
Flowers, Clothes, White
Uncles, Parents, Friends
Rohtak, Haryana, Pui\jab
Engineer, Doctor, People
Thieves, Lawyers, Criminals
Sea, Island, Mountain
Which is the most suitable Venn diagram among the following, which represents
interrelationship among Antisocial elements, Pick pockets and Black mailers ?
©
a ®
(a)
(6)
(c)
(M.B.A. 1997)
(d)
30. Which one of the following four logical diagrams represents correctly the relationship between : Musicians, Instrumentalists, Violinists ?
(LA.S. 1994)
(a)
(6)
(c)
(d)
31. Select from the four alternative diagrams, the one that best illustrates the relationship among the three classes : Pigeons, Birds, Dogs.
(Assistant Grade, 1993)
o « >
(6)
0
o
0
(c)
(d)
D i r e c t i o n s (Questions 32 to 37) : In each of the following questions, choose
the Venn diagram which best illustrates the relationship among three given
items f
©
(a)
32.
33.
34.
35.
36.
37.
38.
(6)
(rf)
Diseases, Leprosy, Scurvy
Hockey, Cricket. Games
Yak, Zebra. Bear
Sun, Moon. Stars
Animals, Men, Plants
Mercury. Mars, Planets
Which of the following figures correctly represents the
Lawyers.
Professionals
(e)
(Hotel Management, 1991)
(Hotel Management, 1991)
(Hotel Management, 1991)
relation between : Doctors,
?
© °?)©
(a)
(6)
(c)
(d)
o
39. Which one of the following sets is best represented in
the adjoining diagram ?
(S.C.RJL 1»94)
(а) Animals, Insects, Cockroaches
(б) Country, States, Districts
(c) Animals. Males, Females and Hermaphrodites
(d) States, Districts, Union Territory
40. Which of the following gives the proper relation of Tall men. Black haired people,
Indians
?
(b)
(a)
-
©
(c)
<5>
<d)
41. If animals that live on land and the animals that live in water are represented
by two big circles and animals that live in water and on land are represented
by small circle, the combination of these three can be best represented as
(a)
(b)
(c)
(d)
Directions (Questions 42 to 44) : In each of the following questions, find
out which of the alternatives (a), (6) (c) or (d) indicates the correct relationship
between the three given words ?
(I. Tax & Central Excise, 1995)
42. Elected house, M.P., M.L.A.
9 ?
^
<23)
(6)
(a)
43. Triangle, Four-sided figure, Square
(a)
©
GO.
D
(c)
®o
(c)-
(6)
44. Doctor, Nurse, Human being
©
(a)
8 o
(b)
(c)
W
(d)
99
99
(d)
(d)
Questions 45 to 53 :
(a)
<W
Indicates that one class is completely contained
in the other but not the third.
Indicates that two classes are completely contained
in the third.
(c)
Indicates that neither class is completely contained
in the other but the two have common members,
forming one entity.
<d)
Indicates that two classes are interrelated
and third one is not.
Directions : Choose the Venn diagram which best illustrates the three
given classes in each question.
45. Protons, Electrons, Atoms
46. Sun, Planets, Earth
(Railways, 1990)
47. Dog, Animal. Pet
48.
49.
50.
51.
Science, Physics, Chemistry
Atmosphere, Hydrogen, Oxygen
Wheat, Grains, Maize
Machine. Lathe, Mathematics
(Railways, 1990)
(C.B.L, 1990)
(Railways, 1990)
52. Biology, Botany. Zoology
53. Citizens, Educated, Men
Directions (Questions 54 to 58) : Each of the questions below contains
three elements. These elements may or may not have some inter se linkage.
Each group of the elements may fit into one of the diagrams at ( a ) , (fr)9 (c),
(cf) and (e). You have to indicate the group of elements which correctly fits
(S.B.I.P.O. 1997)
into the diagrams.
(a)
(6)
Pencil, Stationery, Jeep
Factory, Machinery, Product
Vegetable, Brinjal, Cauliflower
Honesty, Intelligence, Aptitude
Truck, Ship. Goods
D i r e c t i o n s (Questions 59 to 68) : Of the four alternatives in each of the
following questions, three alternatives are such that the three words in each
are related among themselves in one of the five ways represented by (o) 9 (ft),
(c), ( d ) and (e) below while none of these relationships is applicable to the
remaining alternative. That is your answer.
(LJ.C.AAO. 1968)
54.
55.
56.
57.
58.
<g>
(a)
(6)
59. (a) Army, General, Colonel
(c) Painter. Scholar. Table
60. (a) Hen. Dog, Cat
(c) Bed, Ward, Nurse
€1. (a)
(c)
62. (a)
(c)
63. (a)
Atmosphere. Air. Oxygen
Man. Worker, Garden
Animal. Mammal. Cow
Colour, Red. Blue
Body, Hand, Finger
(c) Cereal, Wheat, Rice
(c)
(d)
(e)
(ft) Boy, Student, Player
id) Man, Typist, Peon
(ft) Body. Ear, Mouth
id) Tiger, Animal, Carnivorous
(ft) Boy, Girl. Student
id) Animal, Dog. Cat
(ft) Colour. Cloth. Merchant
(d) Male. Horse, Mare
(ft) Mammal. Nurse. Woman
(rf) Males. Cousins. Nephews
(6) Boy, Girl, Player
64. (a) Bed, Ward, Hospital
(<f) Book, Page, Paragraph
(c) Copper, Zinc, Iron
(6) Professor, Scholar, Politician
6 5 . ' ( a ) Star, Moon, Mars
(d) Swimmer, Carpenter, Singer
(c) Nurse, Doctor, Woman
(6) Mineral, Copper, Wood
66. (a) Periodical, Weekly, Book
(d) Army, Doctor, Engineer
(c) Doctors, Human beings, Married people
(b) Apple, Orange, Mango
67. (a) Director. Engineer, Musician
(d) Oxygen, Air, Water
, (c) Fruit, Mango, Grass
(b) Dean, Painter, Singer
68. (a) Mineral, Iron, Copper
(d) Piston, Engine, Wheel
(c) Seed, Leaf, Root
Directions (Questions 69 to 74) : In each of the following questions, there
are three words which are related in some way. The relationship in each cose
is indicated by one of the four alternatives (a), (5), (c) and (d) given below. The
alternative which best states the relationship is your answer.
(C.A.T. 1997)
(а) P includes part of Q and part of R but Q and R are independent of each other.
(б) P includes Q and part of R but Q is independent of R.
(c) P, Q and R include parts of one another.
(cf) P includes both Q and R.
69. Wheat, Loaf, Barley
70. Singer, Writer, Actor
71. Soldier, Army, Engineer
72. Wood, Steel, Furniture
73. Researcher, Historian, Scholar
74. Tiger, Elephant, Quadruped
Directions (Questions 75 to 78): Given below are five patterns represented
by circles A, B and C which indicate the logical relationship between and
among the respective descriptions. On the basis of description given for A,
B and C respectively in the questions, decide which of the given patterns (a),
(6), (c), (cf) or (e) best indicates the logical relationship.
(a)
(c)
(e)
75.
76.
77.
78.
( A ) Doctor
(B) Male
(C) Actor
(A) Rose
(B) Flower
(C) Lotus
(A) Father
(B) Mother
(C) Child
( A ) Gold
(B) Ornament
(C) Silver
Directions (Questions 79 to 83) : Choose the Venn diagram which best
illustrates the three given classes in each question : (Hotel Management, 1997)
©
(6)
(c)
(d)
79.
80.
81.
82.
83.
Girl. Athlete, Singer
Window, Room, Wall
State, Country, City
Copper, Paper, Wire
Teacher, Graduate, Player
D i r e c t i o n s (Questions 84-85) : Choose the Venn diagram which best illustrates the three given classes in each of the following questions :
( M B A . 1998)
two;
__
(a)
(6)
(stood©
(d)
(c)
(e)
84. Vertebrates, Non-vertebrates, Living beings
85. Women, Teachers, Doctors
86. In a dinner party both fish and meat were served. Some took only fish and some
only meat. There were some vegetarians who did not accept either. The rest
accepted both fish and meat. Which of the following logic diagrams correctly
reflects this situation ?
(IA.8. 1998)
GO
O
(a)
® o
(c)
ANSWERS
Elephants
1. (a):
Wolves
bear no relationship to each
other! But, both of them are animals. (Fig. 1)
Elephants and Wolves
Animals
Fig. 1
2. ( o ) :
All carrots arc vegetables. All vegetables are
foods. (Fig. 2)
Fig. 2
3. (d): All mothers are women. Some mothers and
some women can be widows. (Fig. 3)
Widows
Women
Mothers
Fif. 3
4. (a)
Some authors can be teachers. Some teachers
can be men. Some authors can be men. So, the
given items are partly related to each other.
(Fig. 4)
Authors
Teachers
Men
Fig. 4
5.(b):
All
sparrows
are
But,
birds.
mice
is
Sparrows
Mice
entirely
different. (Fig. 5)
Birds
Fig. 5
Beverages
e.(c)
and Coffee are two separate unrelated items.
But, both of them are beverages. (Fig. 6)
Tea
Tea
Coffee
-
7. (a)
Some
are students. Some students are
athletes. Some boys are athletes. So, the given
items are partly related to each other. (Fig. 7)
boys
Fig. 6
Boys
Student*
Athletes
8.
(c)':
9. (c)
All thieves are criminals. But
different. (Fig. 8)
judge
ia entirely
Both French and German are languages. But,
both of them are different from each other.
(Fig. 9)
French
^
German
Fig. 9
10. (a)
Some
students
cricket players
can be
can
be
cricket
players.
Some
tennis fans.
Some students can be tennis fans. So, the given
items are partly related to each other.
(Fig. 10).
Students
•
Cricket Players
w
Fig. 10
~
Tennis Fans
Quadrilateral*
11. ( a ) :
A l l rhombus a re quadrilaterals.
laterals are polygons (Fig. 11)
A l l quadri
Rhombus
Polygons
F i g . 11
Furniture
12. (d) :
Tables and Chairs are unrelated items. But.
both art? items of Furniture (Pig. 12)
Chairs
Tables
F i g . 12
13. ( c ) :
Tie, Shirt and Pantaloon are separate itema,
entirely different from each other. (Fig. 13)
Shirt
Pantaloon
14. (d) : Dogs and Cats are entirely different from each
other. But, both are pet animals.
(Fig. 14)
Cats
Fig. 14
Vegetable
15. (e):
Brinjal is a vegetable.
different. (Fig. 15)
But Meat
is entirely
Brix\jal
Meat
F i g . 15
Mammals
16. ( 6 ) : Deer and Rabbit are unrelated items. But, both
are mammals (Fig. 16)
Deer^
^
Rabbit
jSsl
F i g . 16
Human beings
17. ( c ) :
A l l teachers and graduates are human beings.
But, some teachers can be graduates and some
graduates can be teachers. (Fig. 17)
T«achersN*
S
F i g . 17
Graduates
18. ( a ) :
Whales, Fishes and Crocodiles are all separate
items, entirely different from each other.
So, they would be represented by three disjoint
circles. (Fig. 18)
19. ie):
All plums are fruits.
different. (Fig. 19)
Whales
Pishes
But, tomatoes are entirely
Pi urns
Tomatoes
F i g . 19
S
20. ( c ) :
Earth
Mountains and Forests are parts of earth. But,
some mountains are forested and some forests
are mountainous. (Fig. 20)
Mountains
Forests
F i g . 20
Carnivores
21. ( 6 ) :
Tiger and Fox are unrelated and entirely different. But, both are carnivores or flesh-eating
animals. (Fig. 21)
22. ( 6 ) : Grams and Beans are entirely different from
each other. But, both are legumes. (Fig. 22)
F i g . 22
Flowers
23. id):
Clothes
Some flowers are white Some clothes are white.
But, all white things are not flowers or clothes.
(Fig. 23)
White
F i g . 23
24. ( a ) :
Uncles, Parents and Friends are entirely different from each other. (Fig. 24)
Uncles
Parents
Friends
F i g . 24
25. ( e ) :
Rohtak ia a p a r t of Haryana. Punjab is a separate state. (Fig. 25)
Haryana
Fig.
>5
•
26. ( 6 ) :
B o t h Engineer a n d Doctor a r e people. B u t ,
both o f t h e m a r e d i f f e r e n t f r o m each o t h e r .
( F i g . 26)
25
s .
People
Engineer
Doctor
Fit. 26
Thieves
2 7 . (e):
All
thieves
a r e criminals.
But,
lawyers
Lawyers
are
entirely different. (Fig. 27)
Criminals
Fig. 27
Island
2 8 . (e):
Island
is
a
part
of Sea.
But,
Mountain
Mountain
ia
entirely different. (Fig. 28)
Sea
Fig.
Pickpockets
29.
(c):
28
Blackmailers
B o t h pickpockets a n d blackmailers a r e antisocial elements.
B u t , s o m e pickpockets can
be blackmailers and v i c e - v e r s a . ( F i g . 2 9 )
Anti-social elements
Fig.
30. ( a ) :
All
violinists
mentalists
are
are
instrumentalists.
musicians.
(Fig.
All
29
Instrumentalist
instru-
Musician
30)
Violinist
Fig.
30
Pigeons
3 1 . (a):
A l l pigeons a r e birds.
But, dogs a r e entirely
different. (Fig. 31)
Birds
V
Fig.
31
Dogs
32. ( a ) :
Both
Leprosy
a n d Scurvy
a r e Diseases.
But,
both are entirely d i f f e r e n t from each other.
(Fig. 32)
Leprosy
Fig. 32
33. ( a ) :
B o t h Hockey and Cricket a r e Games.
B u t , both
Game*
a r e e n t i r e l y d i f f e r e n t f r o m each o t h e r . ( F i g . 3 3 )
Hockey
^
^
Cricket
Flf. 33
34. ( 6 ) :
Yak,
Zebra
and
Bear
are
all different from
each o t h e r . ( F i g . 3 4 )
35. ( c ) :
S u n is a star. Moon is e n t i r e l y d i f f e r e n t f r o m
the t w o . ( F i g . 3 5 )
36. ( c ) :
Men
b e l o n g to the class of animals. Plants
are
entirely d i f f e r e n t from the two. (Fig. 36)
Animals
Fig. 96
anets
37. ( a ) :
Mercury
a n d Mars a r e e n t i r e l y d i f f e r e n t f r o m
e a c h o t h e r . B u t , both a r e planets. ( F i g . 3 7 )
Mercury
V
^
Mars
F i g . 37
38. (c)
:
Both
Doctors
a n d Lawyers a r e Professionals.
B u t , both a r e e n t i r e l y d i f f e r e n t f r o m each
other. ( F i g . 38)
Professionals
Sute
3*. (rf):
Districts
Districts form part of the StaKr. But, Union
Territory is entirely d i f f e r e n t (Pig. 39)
Union Territory
K g . 39
40Ad) :
Some tall men can be black Haired. Some black
haired persons can be Indians.
Some tall men can be Indians.
So, all the three items are partly interrelated.
(Fig. 40)
Tall men
Black haired
Indians
P i g . 40
41. ( 6 ) : Clearly, each one of the animals that live in water and on land, lies in both the
other t w o categories. Also, some of the animals that live on land also live in water.
Elected house
42. ( 6 ) : Clearly, no M P. can be M.L.A. Also, all M P s
and M.L.A.S belong to the elected house.
MP.
M.L.A.
F i g . 41
Four-sided figure
43. ( c ) :
Square is a four-sided figure.
entirely different. (Fig. 42)
Triangle
But, triangle is
Square
F i g . 42
Human beings
44. ( a ) : Doctor and Nurse are entirely different. But,
both are human beings. (Fig. 43)
.u*
Nurse
^
^
TWi.
Doctor
F i g . 43
Atoms
46. ( 6 ) : Protons
and
Electrons
are
entirely different from each other. But, both are partsof
atoms. (Fig. 44)
Protons
Electrons
F i g . 44
46. ( a ) :
Earth belongs to the class of Planets. But, Sun
is entirely different from the two. (Pig. 45)
Earth
Sun
Planets
Fig. 45
47. ( c ) : Some dogs are pets and some pets are dogs.
Both, dog and pets are animals. (Pig. 46)
Animal
Fig. 46
^
48. ( 6 ) :
s .
Science
Physics and Chemistry are entirely different
from each other. But. both belong to the class
of Science. (Fig. 47)
Physics v
Chemistry
Fig. 47
49.(6):
Atmosphere
Hydrogen a n d Oxygen are entirely different
from each other.
But, both are parts of atmosphere. (Fig. 48)
Hydrogen
—^
Oxygen
Fig. 48
Grains
50. ( 6 ) :
Wheat and Maue are two different items.
But, both belong to the class of Grains
(Pig. 49)
Wheat
Maize
Fig. 49
\
51. ( a ) :
Mathematics
Lathe is a type of machine. But, Mathematics
is entirely different from the two. (Fig. 50)
Machine
Fig. 50
62. ( 6 ) :
Biology
Botany and Zoology are entirely different from
each other But, both are branches of Biology.
(Fig. 51)
Botany
53. ( c ) :
S o m e educated a r e citizens.
But,
educated.
both
Men
S o m e citizens a r e
educated
and
are
citizens
men. ( F i g . 5 2 )
Citizens
Educated
Fig. 52
54. ( a ) :
Pencil is an i t e m of Stationery.
entirely different. (Fig. 53)
But,
Jeep
is
Stationery
Jeep
Pencil
Fig. 53
55. (e):
Machinery
a n d product
are
entirely
B u t , both a r e p r e s e n t in a factory.
Factory
different.
(Fig. 54)
Machinery
— ^
Product
Fig. 54
Vegetables
56. ( e ) :
Brinjal
and
Cauliflower a r e
entirely different.
B u t , both a r e vegetables. ( F i g . 5 5 )
Brinjal
Cauliflower
Fig. 55
57. ( d ) :
A p t i t u d e , i n t e l l i g e n c e and h o n e s t y a r e e n t i r e l y
different.
Truck
58. ( c ) :
and
Ship
are
s o m e goods
are
carried
Truck
entirely
by
different.
some
trucks
Goods
But,
and
s o m e goods a r e c a r r i e d by s o m e ships. ( F i g . 5 6 )
Ship
59. ( c ) :
T h i s g r o u p o f i t e m s can b e r e p r e s e n t e d a s i n
F i g . 57.
S i n c e t h e r e is no such d i a g r a m in the q u e s t i o n ,
so (c) is the answer.
Painter
Heo
60. ( a ) : T h i s group of items can be represented aa in
Fig M .
Since there is no such diagram in the question,
so ( a ) is the answer.
Cat
Dog
-Q
Fig. 66
Worker
61. ( c ) : Thin group of item* can be represented aa in
Fig. 69.
Since there is no such diagram in the question,
so (c) is the answer.
Man
Garden
Fig. 69
Colour
62. ( 6 > : This group
in Fig. 60
of items can be represented
Cloth
as
Since there is no such diagram in the question,
no (6) is the answer.
^
Merchant
Fig. 60
Males
Cousins
63. (</) : T h i s group of items can b«» represented as in
Fig. 6 1 .
Since there is no such diagram in the question,
so ( d ) is the answer.
Nephews
Fig. 61
Zinc
64. ( c ) : T h i s group of items can be represented as in
Fig. 62.
Since there is no such diagram in the question.
so (c) is the answer.
Capper
Iron
Fig. 62
Star
Moon
66. ( a ) : T h i s group of items can be* represented as in
Fig 63.
Since there is no such diagram in the question,
so ( a ) is the answer
Fig. 63
Human beings
66. (c): This group of items can be represented as in
Fig. 64.
Since there is no such diagram in the question,
so (c) is the answer.
Married
people
w
W
Fig. 64
Orange
Apple
67. ib): This group of items can be represented as in
Fig. 65.
Since there is no such diagram in the question,
so (b) is the answer.
Mango -
Fig. 66
Seed
68. (c): This group of items can be represented as in
Fig. 66.
Since there is no such diagram in the question,
so (c) is the answer
Leaf
Fig. 66
69. ( a ) :
70. (c):
71. ( a ) :
72. ( a ) :
73. (c):
74. (d) :
75. (a) :
76. (6):
77. (c):
78. ( a ) :
Here P is Loaf, Q is Wheat and R is Barley.
Here P is Singer, Q is Writer and R is Actor.
Here P is Army, Q is Soldier and R is Engineer.
Here P is Furniture, Q is Wood and R is Steel.
Here P is Researcher, Q is Historian and R is Scholar.
Here P is Quadruped, Q is Tiger and R is Elephant.
Some doctors and some actors are males. But, doctor and actor are entirely different.
Both Rose and Lotus are flowers. But, Rose and Lotus are entirely different.
Father, Mother and Child are entirely different.
Some ornaments are made of gold and some of silver. Gold and Silver are entirely
different.
Girls
Athletes
79. (c) : Some girls can be athletes.
Some athletes can be singers.
Some girls can be singers.
' W
Fig. 67
80. (6): Both wall and
But, wall and
window
window
Singers
Room
are parts of a room.
are entirely different.'
Wall
Window
Fig. 68
81. ( a ) : A
city lies
country.
within a
state,
which lies within a
Fig. 69
82. (d): Some
wires
are made of
copper.
But,
Paper
is entirely different.
Teacher
Graduate
83. (c): All three items are partly related to each other.
Player
Fig. 70
84. (6): Both
vertebrates
and
non-vertebrates
are entirely different, but both are
w
Teachers
86. (d): Some teachers and some doctors are women.
But, Teacher and Doctor are entirely different.
living beings.
Doctors
Women
Fig. 71
86. ( a ) : The given situation can be represented as under :
Ate both fish & meat
Ate only fish
Ate only meat
Vegetarians
Fig. 72
TYPE-2
In this type of questions, generally a Venn diagram is given. Each geometrical
figure in the diagram represents a certain class. The candidate is required to study
and analyse the figure carefully and then answer certain questions regarding the
given data.
Example 1 : In the following diagram, three classes of population are
represented by three figures. The triangle represents the school teachers, the
square represents the married persons and the circle represents the persons
living in joint families.
1. Married persons living in joint families but not working as school teachers are
represented by
(a) C
(6) F
(c)D
id) A
Sol. Married persons living in joint families are represented by the region common
to the square and the circle i.e., D and B. But, according to the given conditions,
the persons should not be school teachers. So, B is to be excluded. Hence, the
required condition is denoted by region D. So, the answer is (c).
2. Persons who live in joint families, are unmarried and who do not work as school
teachers are represented by
(a) C
'
(6)B
(c)E
(d) D
Sol. Persons living in joint families are represented by the circle. According to the
given conditions, the persons should be unmarried and not working as school
teachers. So, the region should not be a part of either the square or the triangle.
Thus, the given conditions are satisfied by the region E. So, the answer is (c).
3. Married teachers living in joint families are represented by
(a) C
(6) B
(c)D
(d) A
Sol. Married teachers are represented by the region common to the square and the
triangle i.e.. B and C. But, according to the given conditions, the persons should
be living in joint families. So, the required region should be a part of the circle.
Since B lies inside the circle, so the given conditions are satisfied by the persons
denoted by the region B. Hence, the answer is (6).
4. School teachers who are married but do not live in joint families are represented by
(a) C
(6)F
(c) A
ODD
Sol. As in the above question, married teachers are represented by B and C. But,
here, the given conditions lay down that the persons should not be living in
joint families. So, the required region should lie outside the circle. Since C lies
outside the circle, so the given conditions are satisfied by the persons denoted
by the region C. Hence, the answer is (a).
5. School teachers who are neither married nor do live in joint families are
represented by
(a) F
(6) C
<c)B
(d) A
Sol. School teachers arc represented by the triangle. But according to the given
conditions, persons are neither married nor do they live in joint families. So,
the region should not be a part of either the square or the circle. Such a region
is F. Hence, the answer is (a).
Example 2 : In the following diagram, the square represents girlsp the
circle tall persons, the triangle is for tennis players and the rectangle stands
for the swimmers.
1. Which letter represents tall girls who are swimmers but don't play tennis ?
(a) C
(6) D
(c) G
(d) H
Sol. Tall girls, who are swimmers are represented by the region common to the
square, circle and the rectangle i.e., G and H. But, according to the given conditions, the girls shouldn't be tennis players. So, the required region should not
be a part of the triangle i.e., H should be excluded. Thus, the region representing
the persons satisfying the given conditions is G. Hence, the answer is (c).
2. Which letter represents girls who are swimmers, play tennis but are not tall ?
(a) B
(ft) E
(c) F
(rf) None of these
Sol. Girls who are swimmers and play tennis are represented by the region common
to the square, triangle and rectangle i.e., H. But, it is given that the girls
shouldn't be tall. So, the required region should not be a part of the circle.
Since H is a part of the circle, so the answer is (d).
3. Which letter represents tall girls who do not play tennis and are not swimmers ?
(a) C
(ft) D
(c) E
(d) G
Sol. Tall girls are represented by the region common to the square and the circle
i.e., D, C, J and H. But, according to the given conditions, the girls are neither
tennis players nor swimmers. So, the required region should be neither a part
of the rectangle nor the triangle. G lies inside the rectangle, C inside the triangle and H is common to both. So, the answer is (6).
4. Which letter represents tall persons who are gents and swimmers but do not
play tennis ?
(a) I
(ft) J
ic) K
(d) L
Sol. The tall persons are represented by regions inside the circle i.e., C, D, G, H,
I, J and K. Since the persons are not girls and do not play tennis, so the region
should not be a part of either the square or the triangle. Thus, C, D, G, H
should be excluded. Also, according to the given conditions, the persons should
be swimmers. So, the required region should be a part of the rectangle and
such a region is K. Hence, the answer is (c).
E x a m p l e 3 : The following questions are based on the diagram given
below :
(1) The rectangle represents government employees.
(2) The triangle represents urban people.
(3) The circle represents graduates.
(4) The square represents clerks.
1. Which of the following statements is true ?
ia) All government employees are clerks.
(6) Some government employees are graduates as well as clerks.
(c) Al! government employees are graduates.
(rf) All clerks are government employees but not graduates.
Sol. The above cases may be considered as under :
For statement (a) to be true, the rectangle should lie inside the square. This
is not true. Hence, (a) is false.
For statement (6) to be true, there should be a region common to the rectangle,
circle and the square. Such a region is 6. Hence, (6) is true.
Further, for statement (c) to be true, the rectangle should lie inside the circle.
So, (c) is false.
For statement (d) to be true, square should lie wholly inside the rectangle, with
no region common to the circle. This is not true. So, id) is false.
2. Which of the following statements is true ?
ia) All urban people are graduates.
(6) Some clerks are government employees but not urban.
ic)
id)
All government employees are clerks.
Some urban people are not graduates.
Sol. For the validity of condition (a), the triangle should lie inside the circle. This
is not true. So, (a) is false.
For the validity of statement ib), there should be a region which is common to
the square and the rectangle but is not a part of the triangle. Since no such
region exists, (6) is false.
For the validity of statement (c), the rectangle should lie inside the square.
This is not true. So, ic) is false.
For the validity of statement (d), some region of the triangle should lie outside
the circle. Since this is true, so, id) is true.
3. Choose the correct statement :
ia)
ib)
ic)
id)
Some clerks are government employees.
No clerk is urban.
All graduates are urban.
All graduates are government employees.
Sol. For the validity of statement ia), there should be a region common to the square
and rectangle. Such regions are 6 and 7. So, ia) is true.
Further, for statement ib) to be true, there should be no region common to the
square and the triangle. But since square lies wholly inside the triangle, ib) is
false. For statement ic) to be true, circle should lie inside the triangle. Clearly,
ic) is false. For the validity of statement id), the circle should lie inside the
rectangle. Clearly, id) is false.
EXERCISE 9B
1. Which one of the following statements is correct with regard to the given
figure ?
(S.CJLA 1994)
(а) A and B are in all the three shapes.
(б) E, A, B, C are in all the three shapes,
(c) F, C, D, B, A are in all the three shapes,
(tf) Only B is in all the three shapes.
2. The triangle, square and circle shown below respectively represent the urban,
hard working and educated people. Which one of the areas marked I-VII is
represented by the urban educated people who are not hard working ?
(Civil Services, 1992)
„(
A /
'
HI
sv
VII
( a ) II
(6) I
(c) IV
(d) I I I
Directions (Questions 3 to 6) i In the figure given belowf there are three
intersecting circles each representing certain section of people. Different regions
are marked a—g. Read the statements in each of the following questions and
choose the letter of the region which correctly represents the statement.
Painter
Chine;
Musicians
3. Chinese who are painters but not musicians,
(a) b
(6) c
(c) d
4. Painters who are neither Chinese nor musicians,
(a) b
(6) c
(c) f
5. Chinese who are musicians but not painters,
(a) d
(6) c
(c) b
6. Chinese who are painters as well as musicians,
(a) a
(b) b
(c) c
(<0g
(d)g
(d)
a
(d)
d
Directions ( Q u e s t i o n * 7 to 10) : The figure given below consists of three
intersecting circles which represent sets of students who play Tennis, Badminton
and Volley Ball. Each region in the figure is represented by a small letter.
P
Q
Badminton
Tenni
R ^ — V o l l e y Ball
On
the
basis
of the
above
figure,
answer
the
questions
given
below.
7. Which letter represents the set of persons who play all the three games ?
(a) b
(6) c
(c) f
(d) g
8. Which letter represents the set of persons who play Tennis and Volley Ball but
not Badminton ?
(a) g
(6) e
(c) c
(<f) b
9. Which letter represents the set of persons who play Tennis but neither Badminton nor Volley Ball ?
(o) a
(6) b
(c) c
(d) d
Which letter represents the set of persons who pipy Tennis and Badminton but
not Volley Ball ?
(a) b
(6) c
(c) d
id) f
11. In the given figure, the triangle represents gtrls, the square represents sports
persons and the circle represents coaches. The portion in the figure which
represents girls, who are sports persons but not coaches is the one labelled
10.
(I.A.S. 1996)
A
B
C
(a) A
(b) B
(c) D
(d) E
D i r e c t i o n s (Questions 12 to 16) : Below is given a figure with four intersecting circles, each representing a group of persons having the quality written
against it. Study the figure carefully and answer the questions that follow.
12. The region which represents the people who are intelligent, honest and truthful
but not hard working is denoted by
(a) E
(6) F
(c) H
(d) I
13. The people possessing all the qualities are represented by
(a) I
(6) H
(c) F
(d) E
14. The region which represents people who are not honest but possess all other
three qualities, is denoted by
(a) B
(b) D
(c) F
(d) I
15. People who are not hard working, intelligent and truthful are represented by
(a) G
(b) H
(c) K
{d) L
16. People who are not honest and truthful but are hard working and intelligent
both, are represented by
(a) E
ib) B
(c) M
(d) I
17. If Tall is equivalent to circle, Armymen to triangle and Strong to square, indicate
which number will represent strong armymen ?
(LA.S. 1982)
(a) 3
(6) 4
(c) 5
(,d) 6
D i r e c t i o n s (Questions 18 to 21) : In the figure given below, the circle
represents young persons, the triangle represents uneducated persons and
the rectangle represents employed persons.
Study the figure carefully and answer the questions given below.
18. Which region represents young, uneducated and employed persons ?
(a) 6
(6)5
(c) 4
(d) 3
(e) 2
19. The region which represents educated, employed young persons, is denoted by
(a) 2
(6)3
(c) 4
(d) 5
,
(e) 6
20. WMch region represents young, educated and unemployed persons ?
(a) 7
(6) 4
(c) 1
(rf) 5
(e) 3
21. Which region represents young, uneducated and unemployed persons ?
(a) 1
(6) 2
(c) 6
W) 3
(e) 5
Directions (Questions 22 to 24) : 77ie following questions are based on
the diagram given below. In the diagram, the triangle stands for graduates,
square stands for membership of professional organisations and the circle
stands for membership of social organisations. Read each statement and find
out the appropriate number(s) to represent the people covered by the given
statement.
(Assistant Grade, 1994)
22. Number of graduates in social organisations
(a) 1
(6) 5
(c) 6
(id) 5 and ^
23. Number of graduates in social organisations only
(a) 3
(6) 4
(c) 5
(d) 6
24. Number of graduates in professional organisations
( a ) 5 and 7
(6) 5, 6 and 7
(c) 6 and 7
(d) 4, 5 and 6
25. In the figure given below, triangle represents the women, rectangle represents
the employed and circle represents the doctors, find out the area of the figure
which represents women doctors who are not employed.
(C.B.I. 1993)
(a) 1
(6) 3
(c) 7
(d) 8
26. Study the diagram below and identify the region representing youth who are
employed but not educated.
(S.8.C. 1995)
Youth-
Educated
• Employed
(a) 4 only
(6) 1, 4, 7
(c) 4, 7
(d) 4, 5, 6
27. In the following diagram, parallelogram represents women, triangle represents
sub-inspectors of police and circle represents graduates. Which numbered area
represents women graduate sub-inspectors of police ?
(CJB.I. 1994)
13
5
Jr
sio]
. 8
(a) 5
(6) 3
(c) 8
(d) 13
28. Read the figure and find the region representing persons who are educated and
employed but not confirmed.
(Assistant Grade, 1993)
Educated
Employed
Confirmed in job
(a)
c
(6) a, b, c
(c) b, d
(d)
a, d, c
29. Ip the figure given below, triangle represents the healthy, square represents
the old and circle represents the men. Find out the area of the figure which
represents the men who are healthy but not old ?
(C.B.L 1993)
(a) 1
<
(b)
2
(c)3
(d)
7
Copyrighted materia]
\
30. The diagram below represents the students who study Physics, Chemistry and
Mathematics. Study the diagram and identify the region which represents the
students who study Physics and Mathematics but not Chemistry.
(S.8.C. 1995; I.A-S. 199S)
Physics
Chemistry
Mathematics
(c) V
(d) P + T + S + R + tJ + V
(a) T
(6) P + T + S
D i r e c t i o n s (Questions 31 to 35) : The following five questions are based
on the following diagram in which the triangle represents female graduates,
small circle represents self-employed females and the big circle represents
self-employed females with bank loan facility. Numbers are shown in the
different sections of the diagram. On the basis of these numbers, answer the
(M.BJL 1997)
following :
31. How many
(a) 12
(6) 13
32. How many
(a) 4
(6) 10
33. How many
(a) 9
(6) 11
How
many
34.
(a) 5
(b) 7
35. How many
(o) 3
(b) 8
Directions
answer the questions given below it. The
circle represents players and the triangle
(c) 15
(d) 2 0
(c) 12
(d) 15
(c) 12
(d) 21
(c) 12
(d) 20
(c)9
(d) 12
rectangle represents artists, the
represents doctors.
36. How many
ia) 3
37. How many
ia) 30
38. How many
(a) 3
39. How many
la) 30
40. How many
ia) 22
Directions
players are neither artists nor doctors ?
ib) 8
(c) 22
id)
artists are players ?
id)
(6) 29
(c) 25
doctors are both players and artists ?
id)
(6) 4
(c) 8
doctors are neither players nor artists ?
id)
(6) 27
(c) 22
artists are neither players nor doctors ?
id)
(6) 24
(c) 29
(Questions 41 to 48)
The following questions are
f
9
41.
42.
43.
44.
45.
46.
47.
22
11
8
30
based on
(IA.8. 1985)
the diagram given below :
8
25
V
/
3
12
y ^ 4
11
10\
6
J
7
13
^
14
(1) Rectangle represents males.
(2) Triangle represents educated.
(3) Circle represents urban.
(4) Square represents civil servants.
Who among the following is an educated male who is not an urban resident ?
ia) 4
(6) 5
ic) 9
id) 11
Who among the following is neither a civil servant nor educated but is urban
and not a male ?
ia) 2
(6) 3
ic) 6
id) 10
Who among the following is a female, urban resident and also a civil servant ?
ia) 6
(6) 7
ic) 10
id) 13
Who among the following is an educated male who hails from urban area ?
ia) 4
(6) 2
ic) 11
id) 5
Who among the following is uneducated and also an urban male ?
ia) 2
ib) 3
ic) 11
id) 12
Who among the following is only a civil servant but not a male nor urban
oriented and uneducated ?
ia) 7
ib) 8
ic) 9
id) 14
Who among the following is a male, urban oriented and also a civil servant but
not educated ?
<a) 13
(6) 12
ic) 6
id) 10
48. Who among the following is a male civil servant, who is neither educated nor
belongs to urban area ?
(a) n
ib) 13
ic) 4
id) 1
Directions (Questions 49 to 53): In the following figure, rectangle, square,
circle and triangle represent the regions of wheat, gram, maize and rice
cultivation respectively. On the basis of the above figure, answer the following
questions.
/
5
\
.A
/
3
x x r v
7
2
6
9
j
(
\
10/
11
49. Which area is cultivated by all the four commodities ?
(6)8
(c)9
(d) 2
(a) 7
50. Which area is cultivated by wheat and maize only ?
(a) 8
(6) 6
(c) 5
Id) 4
51. Which area is cultivated by rice only ?
(6) 1
(c) 2
(a) 5
(•d) 11
52. Which area is cultivated by maize only ?
(d) 4
(a) 10
(6) 2
(O 3
?
53. Which area is cultivated by rice and maize and nothing else
(b) 8
(e) 2
(a) 9
(d) 7
Directions (Questions 54 to 63) : In the following figure> the circle stands
for employed9 the square stands for hard working, the triangle stands for
rural and the rectangle stands for intelligent. Study the figure careftilly and
answer the questions that follow.
54. Non-rural, employed, hard working and intelligent people are indicated by region
(a) 8
(b) 9
(c) 10
(d) 11
(e) 12
55. Non-rural, employed people who are neither intelligent nor hard working are
represented by region
( a ) 12
(6) 11
(c) 10
(d) 7
(e) 5
56. Intelligent, employed and hard working non-rural people are indicated by region
( a ) 11
(6)6
(c) 9
(d) 4
(e) 3
57. Hard working non-rural people who are neither employed nor intelligent are
shown by region
(a) 8
(6) 7
(c) 6
(d) 10
(e) 12
58. Employed, hard working and intelligent rural people are indicated by region
59.
60.
61.
82.
(a) 1
(6) 2
(c) 3
(d) 4
(e) 5
Rural hard working people who are neither employed nor intelligent are indicated
by region
(a) 6
(b) 5
(c) 4
(d) 3
(e) 2
Rural employed people who are neither intelligent nor hard working are indicated by region
(a) 2
(6) 4
(c) 6
(d) 9
(e) 10
Rural people who are hard working and employed but not intelligent are indicated
by region
(a) 1
(6) 2
(c) 3
id) 4
(e) 5
Unemployed rural hard working and intelligent people are indicated by region
(a) 1
(6) 2
(c) 3
(d) 4
(e) 5
63. Rural employed people who are neither intelligent nor hard working are indicated
by region
( a ) 10
(6) 9
(c) 6
(d) 4
(e) 2
D i r e c t i o n s (Questions 64 to 67) i In the following figure, the smaller tri•
angle represents the teachers; the big triangle, the politicians; the circlef the
graduates and the rectanglef the members of Parliament. Different regions
are being represented by the letters of English alphabet.
(8.S.C. 1992)
64. Who among the following are graduates or teachers but not politicians ?
( a ) B, G
(b) G, H
(c) A, E
(d) E, F
65. Who among the following politicians are graduates but not the members of
Parliament ?
( a ) B, C
(6) L, B
(c) D f L
(d) A, H, L
66. Who among the following politicians are neither teachers nor graduates ?
(a) E, F
(6) D, E
(c) C, D
(d) L, H
67. Who among the following members of Parliament is a graduate as well as a
teacher ?
(a) G
(b) F
(c) C
(d)
H
D i r e c t i o n s ( Q u e s t i o n s 68 to
diagram
:
The
square
triangle stands
for
for
English-speaking
70) : These questions arc based on
the following
( M . B A . 1998)
Hindi-speaking people,
and
rectangle
for
circle
for
French-speaking,
Gorman-speaking
people.
68. In the above diagram, which one of the following statements is true ?
(a) All French-speaking people speak German.
(b) All French-speaking people speak English.
(c) All German-speaking people speak English and Hindi.
id) All French-speaking people speak Hindi also.
69. In the diagram, which one of the following statements is true ?
(a) There are some people who speak all four languages.
(b) Some German-speaking people can speak either Hindi or English.
(c) Some English-speaking people cannot speak all the languages.
(d) All Hindi-speaking people speak French but not German.
70. In the above diagram, which one of the following statements is not true ?
(a) German-speaking people cannot speak French.
(b) No French-speaking people can speak German.
(c> Some Hindi-speaking people can speak French, English and German as well.
id) Some French-speaking people can speak Hindi and English but not German.
D i r e c t i o n s (Questions 71 to 75) : The following figure represents a set of
persons — the
triangle
represents educated
persons,
the rcctangle represents
policcmcn,
the bigger ellipse represents road
tax payers and smaller ellipse
represents shopkeepers.
(Delhi Police, 1988)
The
following
questions
arc
based
on
the
above
diagram.
71. Looking at the given figure, it can be said that
(a) some persons who are neither shopkeepers nor policemen are educated.
(b) some persons who are either shopkeepers or policemen, pay road tax, though
uneducated.
(c) some persons who are either shopkeepers or policemen pay road tax and
are also educated.
(d) all the above statements are correct.
72. According to this figure, it follows that
(a) policemen do not pay road tax.
(b) shopkeepers do not pay road tax.
(c) some shopkeepers are educated.
(d) some policemen are shopkeepers.
73. From the above figure, it can be concluded that
(а) all educated policemen pay road tax.
(б) all educated shopkeepers pay road tax.
(c) all road tax paying policemen are educated.
.
(d) all road tax paying shopkeepers are educated.
74. Looking at the given figure, it can be said that
(а) some of the uneducated policemen pay road tax.
(б) some of the educated shopkeepers pay road tax.
(c) some of the road tax payee policemen are shopkeepers too.
(d) some of the road tax payee shopkeepers are policemen too.
78. On the basis of this figure, it can be concluded that
(а) none of the educated shopkeepers is a policeman though an uneducated
policeman is a shopkeeper.
(б) some of the educated shopkeepers are road tax payers even though they
discharge duties of a policeman.
(c) some of the educated policemen who pay road tax are sharing profits with
uneducated shopkeepers.
(d) none of the educated shopkeepers is a policeman nor an educated policeman
a shopkeeper.
ANSWERS
1. ( d ) :
B is the region common to the circle, square and triangle.
2. ( c ) : T h e required region is the one which is common to the triangle and the circle but
is not a part of the square i.e. IV.
3. ( a ) : T h e required region is the one which is common to the circles A and B and lies
outside circle C i.e. b.
4. ( c ) : T h e required region is the one which lies inside the circle B but is not a part of
either circle A or circle C i.e. f.
t*. ( a ) : T h e required region is the one which is common to the circles A and C but is not a
part of circle B i.e. d.
6. ( c ) : T h e required region is the one common to all the three circles i.e. c.
7. ( 6 ) : T h e required region is the one common to all the three circles Le. c.
8. (d): T h e required region is the one which is common to circles P and R but is not a part
of circle Q. i.e. b.
9. ( a ) : T h e required region is the one which lies inside circle P but is not common to circle
Q or circle R or both i.e. a
10. ( c ) : T h e required region is the one which is common to circles P and Q but lies outside
circle R Le.f d.
11. ( 6 ) : T h e required region is the region which is common to the triangle and square but
lies outside the circle Le., B,
12. ( c ) : The required region is the one which is common to the circles 2, 3 and 4 Hut is not
a part of circle 1 Le. H.
13. Id): T h e required region is the one which is common to all the four circles i.e. E.
14. ( c ) : T h e required region is the one which is common to the circles 1, 2 and 4 but lies
outside circle 3 i.e. F.
15. ( d ) : The required region is the one which doe® not lie inside circle* 1, 2 and 4. Le. L
16. ( b ) : T h e given conditions are satisfied by the persons denoted by the region which is
common to circles 1 and 2 but is not a part of either circle 3 or circle 4 i.e. B
17. ( 6 ) : Strong armymen will be represented by the region which is common to the square
and t h * triangle but lies outside the circle i.e. 4.
18. ( c ) : T h e given set of persons is denoted by the region common to the circle, the triangle
and the rectangle Le. 4.
19. ( a ) : T h e given set of persons is denoted by the circular region contained in the rectangle
but outside the triangle i.e. 2.
20. ( c ) : T h e given set of persons is denoted by the circular region outside the triangle and
the rectangle i.e. 1.
21. ( d ) : T h e given set of persons is denoted by the circulai region inside the triangle and
outside the rectangle i.e. 3.
,
22. id): The required region is the one common to the circle and triangle i e . regions 5 and 6.
23. ( d ) : T h e required region is the one which is common to the triangle and circle but lies
outside the square U 6.
24. ( a ) : The required region is the one common to the triangle and square Le. regions ft and 7.
25. ( c ) : T h e required region is the one which is common to the triangle and circle but lies
outside the rectangle Le. 7.
26. ( o ) : The required region is the one which is common to the circles A and C but lies
outside circle B i.e. 4.
27. (6) : The required region is the one common to the parallelogram, triangle and circle i.e. 3.
28. ( c ) : The required region is the one which is common to the two circles but lies outside
the triangle i.e., regions b and d.
29. (b) : T h e required region is the one which is common to the triangle and circle but t i e s
outside the square i.e. 2.
30. la) : T h e required region is the one which is common to circles X and Z but lies rtitside
circle Y Le. T.
31. ( d ) : T h e region common to the triangle and any of the two circles represents the number
of self-employed female graduates. It is 8 + 5 + 7 = 20.
32. ( a ) : The region lying inside the triangle but outaide both the circles represent* the number
of f e m a l e graduates who are not self-employed. It is 4.
33. ( d ) : T h e regions lying outside' the triangle but inside any of the two circleaj-epresenni
the number of non-graduate, self-employed females. It is (9 + 3 + 6 + 2 + 1) = 21.
' 34. ( c ) : T h e region common to the triangle and the bigger circle represent* the number of
self-employed female graduates with bank loan facility. It is 7 + 5 « 12.
35. < c ) : The region lying outside the triangle but inside the bigger triangle represents the number
of non-graduate self-employed females with bank loan facility. It is (6 • 2 + 1) = 9.
36. ( d ) : T h e region lying inside the circle but outside the triangle and the rectangle represents
the numKer of players who are neither artists nor doctors. It is 25.
37. (c): The region common to the circle and the rectangle represents the required set of
persons. Thus, number of artists who are players = (22 + 3 ) » 25.
38. (a): The region common to the circle, triangle and the square represents the required
set of persons. Thus, number of doctors who are both players and artists x 3.
39. (6): The region which lies inside the triangle but outside the circle and the rectangle
represents the persons satisfying the given conditions. Thus, number of doctors who
are neither players nor artists = 27.
40. (d) : The region which lies inside the rectangle but outside the triangle and the circle
represents the required set of persons. Thus, number of artists who are neither players
nor doctors = 30.
41. id): The person satisfying the given conditions is represented by the region which is
common to the triangle and the rectangle but lies outside the circle i.e. 11.
42. (ft): The person satisfying the given conditions is represented by the region which lies
inside the circle but outside the square, the rectangle and the triangle i.e. 3.
43. (c): The person satisfying the given conditions is represented by the region which lies
outside the rectangle and is common to the circle and the square i.e. 10.
44. ( a ) : The person satisfying the given conditions is represented by the region which is *
common to the triangle and the rectangle and also lies inside the circle i.e. 4.
45. (d) : The person satisfying the given conditions is represented by the region which lies
outside the triangle and is common to the circle and the rectangle i.e. 12.
Remember : The condition which is not mentioned shouldn't be considered or
assumed. For instance, here, 6 also denotes the required region. But since it lies
inside the square and there is no mention of'civil servant', so it canrot be the answer.
46. ( a ) : The person satisfying the given conditions is denoted by the region which lies inside
the square but outside the circle, rectangle and triangle i.e. 7.
47. (c): The person satisfying the given conditions is denoted by the region which is common
to the rectangle, circle and the square but lies outside the triangle Le. 6.
48. (6): The person satisfying the given conditions is represented by the region common to
the rectangle and the square but lying outside the triangle and the circle i.e. 13.
49. ( a ) : The required region is the one common to the rectangle, square, circle and the triangle i.e. 7.
50. ( d ) : The required region is the one which is common to only the rectangle and the circle
and is not a part of either the triangle or the square i.e. 4.
51. (ft): The required region is the one which lies inside the triangle and outside the rectangle,
square and circle i.e. 1.
52. (c): The required region is the one which lies inside the circle but outside the rectangle,
square and triangle Le. 3.
53. (c): The required region is the one which is common to only the triangle and the circle
i.e. 2.
54. (ft): The required set of people is represented by the region which lies outside the triangle
and is common to the circle, square and rectangle i.e. 9.
55. (d): The required set of people is represented by the region which lies outside the triangle,
inside the circle but outside the rectangle and the square i.e. 7.
56. (c): The required set of people is represented by the region which is common to the
rectangle, circle and square but lies outside the triangle i.e. 9.
57. (e): The required set of people is denoted by the region which lies inside the square but
outside the triangle, circle and rectangle i.e. 12.
58. ( a ) : The required set of people is denoted by the region common to the circle, square,
rectangle and triangle Le. 1.
59. (rf): The required set of people is represented by the region which is common to the
triangle and the square but lies outside the circle and rectangle i.e. 3.
60. ( c ) : T h e required set of people is denoted by the region which is common to the triangle
and the circle, but is not a part of either the rectangle or the square i.e. 6.
61. ( 6 ) : T h e required set of people is represented by the region which is common to the
triangle, square and circle but is not a part of the rectangle i . e 2.
62. ( d ) : T h e required set of people is represented by the region which lies outside the circle
and is common to the triangle, square and rectangle i.e. 4.
63. ( c ) : T h e required set of people is denoted by the region which is common to the triangle
and circle but is not a part of either the rectangle or the square Le. 6.
64. ( c ) : T h e persons satisfying the given conditions are denoted by regions which lie inside
the smaller triangle or the circle but outside the bigger triangle i e . A and B.
65. ( a ) : T h e persons satisfying the given conditions are represented by regions which are
common to the triangle and the circle but lies outside the rectangle Le. B and C.
66. ( d ) : T h e persons satisfying the given conditions are represented by regions which lies
inside the bigger triangle but outside the smaller triangle and the circle i.e. L
and H 67. ( 6 ) : T h e person satisfying the given conditions is represented by the region common to
the rectangle, circle and the smaller triangle i.e. F.
68. ( d )
69.
(6)
70. (c)
71. ( d )
72. (c)
73. (c)
74. ( 6 )
75. ( d )